Problem: Simplify the following expression: $y = \dfrac{r^2 - 6r - 27}{r + 3} $
Answer: First factor the polynomial in the numerator. $ r^2 - 6r - 27 = (r + 3)(r - 9) $ So we can rewrite the expression as: $y = \dfrac{(r + 3)(r - 9)}{r + 3} $ We can divide the numerator and denominator by $(r + 3)$ on condition that $r \neq -3$ Therefore $y = r - 9; r \neq -3$